Versatile Control of $^{9}{\mathrm{Be}}^{+}$ Ions Using a Spectrally Tailored UV Frequency Comb

Versatile Control of ${}^{9}{Be}^{+}$ Ions Using a Spectrally Tailored UV Frequency Comb

A.-G. Paschke, G. Zarantonello, H. Hahn, T. Lang, C. Manzoni, M. Marangoni, G. Cerullo, U. Morgner, and C. Ospelkaus

Phys. Rev. Lett. 122, 123606 – Published 29 March 2019

Abstract

We demonstrate quantum control of ${}^{9}{Be}^{+}$ ions directly implemented by an optical frequency comb. Based on numerical simulations of the relevant processes in ${}^{9}{Be}^{+}$ for different magnetic field regimes, we demonstrate a wide applicability when controlling the comb’s spectral properties. We introduce a novel technique for the selective and efficient generation of a spectrally tailored narrow-bandwidth optical frequency comb near 313 nm. We experimentally demonstrate internal state control and internal-motional state coupling of ${}^{9}{Be}^{+}$ ions implemented by stimulated-Raman manipulation using a spectrally optimized optical frequency comb. Our pulsed laser approach is a key enabling step for the implementation of quantum logic and quantum information experiments in Penning traps.

Received 6 June 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.123606

Physics Subject Headings (PhySH)

Atom & ion cooling Coherent control Penning traps Quantum description of light-matter interaction Second order nonlinear optical processes Ultrashort pulses

Atomic, Molecular & Optical

Authors & Affiliations

A.-G. Paschke^1,2, G. Zarantonello^1,2, H. Hahn^1,2, T. Lang¹, C. Manzoni³, M. Marangoni³, G. Cerullo³, U. Morgner¹, and C. Ospelkaus^1,2

¹Institute of Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
²Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
³IFN-CNR, Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, Milano, 20133, Italy

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Vol. 122, Iss. 12 — 29 March 2019

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Figure 1
Illustration of the two-photon stimulated Raman process implemented by two beams from a single mode-locked laser for ${}^{9}{Be}^{+}$ ions at a ground state sublevel splitting of $ω_{0} (B = 5 T) \approx 2 π \times 139 GHz$ . (a) Raman transitions occur by absorption of a photon from off-resonant comb teeth of beam 1 and stimulated emission into off-resonant comb teeth of beam 2. We reference detunings to the ${}^{2}{P_{1 / 2}}$ level, as illustrated for the first comb’s central frequency $ω_{c 1}$ , $Δ_{ω c 1}$ . (b) Illustration of the relative frequency shift $Δ ω$ between both beams, required to fulfill the Raman resonance condition for internal-motional coupling.
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Figure 2
Numerical simulations showing the influence of the comb’s spectral properties on achievable Raman coupling strengths for different applied magnetic fields. (a) Average laser power $P_{av, req}$ required in order to achieve a spin flip within $t_{π} = 5 μ s$ (calculated as in Ref. [1]) while ensuring the total scattering probability to be $(Γ_{total 1} + Γ_{total 2}) \times 5 μ s = 10^{- 4}$ as a function of the UV comb’s spectral bandwidth $δ ω_{FWHM}$ . (b) Corresponding required detuning $Δ_{ω} / 2 π$ of the comb’s central frequency as a function of $δ ω_{FWHM}$ . The total scattering rate of beam $j$ is composed of Raman and (decohering) elastic Rayleigh scattering [13] according to $Γ_{{total}_{j}} = 1 / 2 [Γ_{{Raman}_{j}} (↓) + Γ_{{Raman}_{j}} (↑) + Γ_{{el}_{j}}]$ , with $Γ_{{Raman}_{j}}$ and $Γ_{{el}_{j}}$ calculated following Ref. [13] with the squared electric field amplitudes replaced by the sum over all contributing comb modes. Data for different magnetic fields are shown each for a sinc-shaped spectrum, either unmodified (solid) or spectrally cut outside the main peak (dotted) or the second side-maxima (sm) (dashed). The lines are guides to the eye. Assumed were time-bandwidth limited pulses and a focal radius of $15 μ m$ . The sinc-shaped spectrum approximates the unmodified spectrum of our UV frequency comb but is also representative of a more general pulse shape which typically exhibits spectral side maxima.
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Figure 3
Focus-dependent spectral compression technique implemented during SHG from broadband pulses near 626 nm into narrow-bandwidth pulses near 313 nm using a 4.5 mm long BiBO crystal in single pass configuration. (a) Resulting UV SH bandwidth as a function of the focal radius of the FF beam along the relevant direction of spatial walk-off (horizontal). (b) Effective conversion efficiencies for an average input power of 400 mW as a function of the horizontal focal radius of the FF beam. For the rectangular cut crystal a circular focus was present, whereas for the Brewster cut crystal the focal dimension in the transverse direction by geometry was reduced by approximately a factor of $n_{BiBO} \approx 1.88$ , thereby enhancing conversion efficiencies for a given horizontal radius. The solid lines correspond to simulation results obtained with the model described in Ref. [14]. We assume transform-limited Gaussian input pulses with an initial bandwidth of $Δ λ = 1.5 nm$ in (a) and $Δ λ = 0.9 nm$ in (b).
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Figure 4
(a) Illustration of spectral pulse modification technique. Razor blades located directly behind the SHG crystal address and block the comb’s unwanted spectral wings, which are spatially separated due to spatiotemporal coupling effects causing an angularly dispersed UV signal. (b) Sample modified UV spectrum. In black the unfiltered UV spectrum is shown, with its asymmetric shape dominated by the spectral shape of the customized fiber-based frequency comb. The blue and red spectra correspond to different positions of the razor blades independently moved (with decreasing distance) on each side of the spatial walk-off plane without affecting the intensity of the main peak.
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Figure 5
Direct pulsed laser quantum control of ${}^{9}{Be}^{+}$ ions. (a) Numerical simulations [similar to Fig. 2] comparing achievable Raman coupling strengths for different magnetic field regimes. In green for the Paschen-Back regime with a magnetic field of 5 T and in orange for the low-field Zeeman regime with a magnetic field of 22.3 mT, each with differently modified spectra as discussed in Fig. 2. (b) A spectrally tailored UV pulse train is divided into two beam paths and focused onto the ion from orthogonal directions and synchronized in arrival time using a temporal delay stage. (c) Single beam induced carrier Rabi oscillations on the $| 2, 0 ⟩ \leftrightarrow | 1, 0 ⟩$ transition implemented using only the first Raman beam with AOM1. Shown is the population of the $| 2, 0 ⟩$ state as a function of the laser probe duration. Decoherence is expected to be dominated by the strong magnetic field noise sensitivity of the transition of $12.53 MHz / mT$ . The comb’s applied spectral bandwidth of the main peak was $δ ω_{FWHM} \approx 2 π \times 940 GHz$ and its detuning $Δ_{ω c 1} \approx 2 π \times 1.26 THz$ , with both values optimized according to the achievable UV pulse generation, shaping, and Raman coupling performance. (d) Resonance scan of a red sideband transition on the $| 2, 1 ⟩ \leftrightarrow | 1, 1 ⟩$ transition for the ion’s axial motional mode ( $ω_{m, axial} = 2 π \times 0.892 MHz$ ), driven by the interaction of both Raman beams with a frequency shift of $Δ ω_{AOM} = 2 π \times 382.7366 MHz$ . Shown is the population of the $| 1, 1 ⟩$ state as a function of a frequency shift applied to AOM1. The red sideband transition probability is due to the Doppler cooled motional state of the ion.
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Physical Review Letters

Versatile Control of Be+9 Ions Using a Spectrally Tailored UV Frequency Comb

A.-G. Paschke, G. Zarantonello, H. Hahn, T. Lang, C. Manzoni, M. Marangoni, G. Cerullo, U. Morgner, and C. Ospelkaus

Phys. Rev. Lett. 122, 123606 – Published 29 March 2019

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Versatile Control of ${}^{9}{Be}^{+}$ Ions Using a Spectrally Tailored UV Frequency Comb